How to keep app save data?

3rd party app data are stored as part of the iPhone backup made by iTunes (separately from the apps themselves). The only way to get the data back is to restore from that backup. But, since iTunes only keeps one backup, overwriting the previous one at each sync, if you've removed the app from the phone the data for that app will be deleted at the next sync.

So, _you need to leave the app(s) on the phone_ to preserve their data. The alternative is really unworkable - make backup copies of the iPhone backup file (location is given HERE) before you delete an app; it's unworkable because if you go back to that backup for a restore, you'll lose any changes to other apps/settings, pics, messages, etc., since the date of that backup.

3rd party app settings and data created and stored by a 3rd party app is included with your iPhone's backup, which is updated as the first step during the iTunes sync process. 3rd party app settings and data created and stored by each app is "sandboxed" with the app. If you delete the app from your iPhone, the app settings and any data created and stored by the app is deleted from the iPhone with the app.

If your iPhone's backup has been updated since a 3rd party app was removed from your iPhone, the app settings and any data created and stored by the app will no longer be available with your iPhone's backup. If not, you can restore your iPhone with iTunes from your iPhone's backup followed by re-installing the app.

Application data is stored in two places: on your phone & your phone's backup. Removing an application from your phone also removes it's saved data. The only way to restore that data would be to restore your phone from a backup that contained said application data, assuming you haven't synced since removing the application from your phone, as the first step in a sync is a backup which would overwrite the previous backup saved on your computer.